Metaphor example: The ship plowed through the sea (using plowed instead of navigated).

Metonymy example: The sails crossed the ocean (using sails instead of ship with sails).

In cognitive linguistics, metonymy refers to the use of a single characteristic to identify a more complex entity and is one of the basic characteristics of cognition. It is common for people to take one well-understood or easy-to-perceive aspect of something and use that aspect to stand either for the thing as a whole or for some other aspect or part of it.
Cognitively, metonymy is attested in cognitive processes underlying language (e.g. the infant's association of the nipple with milk). Objects that appear strongly in a single context emerge as cognitive labels for the whole concept, thus fueling linguistic labels such as "sweat" to refer to hard work that might produce it.
The word metonymy is derived from the Greek μετωνυμία (metōnymia) "a change of name"
Metonymy works by the contiguity (association) between two concepts, whereas metaphor works by the similarity between them. When people use metonymy, they do not typically wish to transfer qualities from one referent to another as they do with metaphor: there is nothing press-like about reporters or crown-like about a monarch, but "the press" and "the crown" are both common metonyms.
Two examples using the term "fishing" help make the distinction clear (example drawn from Dirven, 1996). The phrase "to fish pearls" uses metonymy, drawing from "fishing" the idea of taking things from the ocean. What is carried across from "fishing fish" to "fishing pearls" is the domain of usage and the associations with the ocean and boats, but we understand the phrase in spite of rather than because of the literal meaning of fishing: we know you do not use a fishing rod or net to get pearls and we know that pearls are not, and do not originate from, fish.

In contrast, the metaphorical phrase "fishing for information", transfers the concept of fishing into a new domain. If someone is "fishing" for information, we do not imagine that he or she is anywhere near the ocean, rather we transfer elements of the action of fishing (waiting, hoping to catch something that cannot be seen) into a new domain (a conversation). Thus, metonymy works by calling up a domain of usage and an array of associations (in the example above, boats, the ocean, gathering life from the sea) whereas metaphor picks a target set of meanings and transfers them to a new domain of usage.
The concept of metonymy also informs the nature of polysemy — i.e. how the same phonological form (word) has different semantic mappings (meanings). If the two meanings are unrelated, as in the word pen meaning writing instrument versus enclosure, they are considered homonyms.

Within logical polysemies, a large class of mappings can be considered to be a case of metonymic transfer (e.g. chicken for the animal, as well as its meat; crown for the object, as well as the institution). Other cases where the meaning is polysemous however, may turn out to be more metaphorical, e.g. eye as in the eye of the needle.
When the distinction is made, it is the following: when A is used to refer to B, it is a synecdoche if A is a component of B and a metonymy if A is commonly associated with B but not actually part of its whole.
Thus, "The White House said" would be a metonymy for the president and his staff, because the White House (A) is not part of the president or his staff (B) but is closely associated with them. On the other hand, asking for "All hands on deck" is a synecdoche because hands (A) are actually a part of the people (B) to whom they refer.
Those who argue that synecdoche is a class of metonymy might point out that "hands" (A) are a metonym for workers (B) since hands are closely associated with the work the people do as well as literally, a physical part of the people. That is, hands are associated with work through a metonymy at the same time as being associated with the people through synecdoche.
An example of a single sentence that displays synecdoche, metaphor and metonymy would be: "Fifty keels ploughed the deep", where "keels" is the synecdoche as it names the whole (of the ship) after a particular part (of the ship); "ploughed" is the metaphor as it substitutes the concept of ploughing a field for moving through the ocean; and "the deep" is the metonym, as "depth" is an attribute associated with the ocean.